Review of Discrete Element Method Simulations of Soil Tillage and Furrow Opening
Abstract
:1. Introduction
2. Modelling Agricultural Soils with DEM
2.1. DEM Contact Models
2.1.1. Linear Spring Contact Model
2.1.2. Hertz–Mindlin Contact Model
2.1.3. Hysteretic Spring Contract Model
2.1.4. Accounting for Cohesion with DEM Contact Models
Linear Cohesion Model
Parallel Bond Model
Johnson–Kendall–Roberts Cohesion
Reference | Relative Error in DEM Prediction (%) Relative to Measured Data | Travel Speed (km h−1) | Operating Depth (mm) | Tillage Tools | Soil Texture | Dry Bulk Density (kg m−3) | Soil Water Content (%, w/w) | Cohesive Strength (kPa) | Contact Model | |
---|---|---|---|---|---|---|---|---|---|---|
Draught | Vertical Force | |||||||||
Sadek et al. [58] | n/a | n/a | n/a | n/a | n/a | Sandy soil | 990 1280 1360 1500 | 0.02 13 21.5 | 1.23-32.70 | PBM |
Chen et al. [7] | 4 to 31 | n/a | 3.19 (average) | 100 | Sweep tine | Coarse sand Loamy sand Sandy loam | 1410 1330 1410 | 8.98 14.84 18.2 | 15.7 25.2 36 | PBM |
Obermayr et al. [52] | n/a | n/a | 2.16–4.5 | 10–200 | Bulldozer blade | n/a | 1900 | n/a | 11.16 | LSCM + cohesion |
Tamas et al. [30] | 4 to 12 | n/a | 1.8–8.64 | 200 | Sweep tine | Sandy soil | 1850 | 6.33 | 11.86 | PBM |
Bravo et al. [18] | 9, 24 | n/a | - | 150–500 | Para-plough and mouldboard plough | Clay (Vertosol) | 1000 1200 1400 | 8 18 20 35 | 25–125 | LSCM + cohesion |
Li et al. [56] | 3 to 15 | n/a | 3.6 | 180–260 | Subsoiler | n/a | n/a | 19 | n/a | PBM |
Mak and Chen [61] | n/a | n/a | 2.2–6.59 | 50–200 | Sweep tine | Loamy sand | 1320 | 11.3 | 13.9 | PBM |
Obermayr et al. [72] | n/a | n/a | 100–200 | Straight-vertical blade and bulldozer blade | Sand | 1520 1980 1870 | 10 15 | 6–22.5 | LSCM + cohesion | |
Ucgul et al. [38] | ≤11.6 | ≤15.2 | 5–12.5 | 70 | Sweep tine | Sandy loam | 1750 | 8 | 6 | HSCM |
Ucgul et al. [53] | n/a | n/a | 4–12 | 75 | Sweep tine | Sandy loam | 1320 1780 1880 | 1 15 13 | 3 15 22 | HSCM + LCM |
Kotrocz et al. [60] | n/a | n/a | n/a | 50–150 | Cone penetrometer | Loamy sand | 1632 | 15.8 | 6.61–8.66 | PBM |
Li et al. [70] | 2.99 | 3–18 | Claw | Sandy loam | 1300 | n/a | 17.5 | PBM | ||
Murray [69] | 1.86 | 50.7 | 8 | 38 | Disc and hoe openers | Clayey lacustrine | 1560 | 19.6 | n/a | PBM |
Hang et al. [32] | n/a | n/a | 3 | 300 | Subsoiler | Loamy clay | 1346 | 12.5 | 11.8 | PBM |
Milkevych et al. [62] | n/a | n/a | 3.2 | 100 | Sweep tine | Coarse sand Loamy sand | 1410 1330 | 9 14.8 | 15.8 25.1 | PBM |
Tekeste et al. [55] | 9, 12 | -59, -49 | 0.79–9.65 | 102 | Sweep tine | Loam | 1307 | 8.99 | 33 | PBM |
Tong et al. [73] | <10 | <10 | 7.2 | 300–450 | Subsoiler (straight shank-sweep tine, curved shank-chisel tine, curved shank-sweep tine, bentleg-chisel tine) | n/a | 1230–1420 | n/a | n/a | not stated |
Kim et al. [44] | 5.16 to 9.9 | n/a | 7.64–7.9 | 5–200 | Mouldboard plough | Loam | 1496–1904 | 24.5–34.02 | n/a | EEPA |
Aikins et al. [41] | 5 to 31 | 8, 20 and greater | 8 | 100 | Bentleg and narrow point openers | Clay (Vertosol) | 1504 | 23.7 | 46.4 | HSCM + LCM |
Wang et al. [74] | 15.08 | n/a | 3 | 300 | Winged subsoiler | Sandy loam | 1404–1833 | n/a | n/a | PBM |
Sadek et al. [75] | ≤20.2 | n/a | 4–16 | 127 | Disc | Sandy loam | 1700 | 16.32 | n/a | PBM |
Saunders et al. [76] | n/a | n/a | 4.5–10 | 25–100 | Plough skimmers | Sandy loam | 1523.8 | 8.3 | n/a | HSCM + LCM |
Ma et al. [77] | 2.88 to 5.97 | n/a | 1.08–2.16 | 120 | Scraper | Sandy loam | 1389 | 10 | n/a | not stated |
Hoseinian et al. [35] | 2 | 2.5 | 0.9 | 150 | Dual sideway-share | Sandy clay loam | 1565 | 11.5 | 15.4 | PBM |
Edinburgh Elasto-Plastic Adhesion Model
2.2. Particle Size and Shape
3. Calibration Techniques for Determining DEM Input Parameters
3.1. Angle of Repose Test
3.2. Inclined Plane Test
3.3. Direct Shear Test
3.4. Triaxial Compression Test
3.5. In Situ Approaches
4. Prediction of Soil Failure, Loosening, and Disturbance Parameters
4.1. Soil Failure and Loosening
- Minimum particle displacement caused directly by an opener occurs with particles just adjacent to the bottom part of the opener (for wide tines) or particles aligning the walls of the slot below critical depth (for narrow tines).
- To establish a sharp contrast between displaced and undisturbed particles, particle locations immediately after particle loosening (i.e., before the particle settle) has to be used.
4.2. Soil Movement and Disturbance Parameters
5. Prediction of Tillage Forces
6. Soils Modelled in DEM Simulations
7. Conclusions
- Even though the Hertz–Mindlin contact model (HMCM) has been used in most DEM studies of tillage and furrow opening, it consistently fails to predict vertical soil force accurately. The Hysteretic Spring contact model (HSCM) can more accurately predict soil forces and particle movement.
- Angle of repose, inclined plane, direct shear, triaxial compression, and some in situ tests (grouser shear, plate sinkage, and cone penetration tests) have been used to measure and calibrate DEM input parameters. The angle of repose test has been used mainly for cohesionless soils due to the poor flowability of cohesive soils. However, using results from reproducible phases of the angle of repose experiment, successful calibrations for cohesive soils have been achieved.
- Unlike other numerical models, DEM is able to closely predict not only soil forces, but it is also capable of modelling soil failure mechanisms, soil loosening, and soil particle movement. Soil rupture and crack propagation, critical depth, three-dimensional particle movement within the soil profile and lateral particle movement on top of the soil have all been predicted in DEM.
- Using voidage or porosity grids to determine loosened furrow cross-sectional profiles has been found to be superior to using particle velocity and displacement profiles. However, some researchers have successfully used a particle displacement approach to determine accurate furrow profiles with a more objective criteria for defining loosened furrow boundary.
- Close predictions of draught and vertical forces (≤20%) have been obtained with DEM. These predictions can be improved by using smaller particles of a near-real shape. However, this must be balanced with computation time requirements.
- The Edinburgh elasto-plastic adhesion model (EEPA) has been successfully used to model consolidated or cohesive powders. This contact model is recommended to be studied more extensively for cohesive soils, although some researchers have used it.
- Due to pore water pressure within wet and soft soils, coupling DEM and CFD is likely to produce more accurate simulations. This idea can be explored in future research.
- A comprehensive analysis of soil disturbance parameters has been successfully done using voidage grids in EDEM® DEM software. Replication of this approach in other DEM software is recommended.
- The criteria introduced by Aikins et al. [41] for defining particle displacement threshold for DEM furrow profile identification need further investigation with particles of smaller radii than the 5 mm used in the study. This approach can provide greater details on the three-dimensional soil translocation process.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
γ | Surface energy (J/m2) |
Linear overlap | |
Normal component of relative velocity | |
Tangential component of relative velocity | |
Cohesive stress | |
Linear relative velocity | |
Tangential component of overlap | |
Friction coefficient | |
Internal friction angle between the particles (Degree) | |
µr | Coefficient of rolling friction |
µs | Coefficient of static friction |
A | Cross-sectional area of the shear box |
a | JKR contact radius |
c | Soil cohesion (Pa) |
ca | Soil–metal adhesion (Pa) |
d | Working depth (m) |
dn | Damping coefficient |
dt | Tangential component of damping coefficient |
e | Coefficient of restitution of the particles |
E | Young’s modulus |
Eeq | Equivalent Young’s modulus |
F | Contact force |
Fa | Normal force in direct shear test |
Fb | Horizontal (shearing) force in direct shear test |
Fca | Cohesive or adhesive force |
Fd | Damping force |
Fn | Normal contact force |
Fs | Spring force |
Ft | Tangential component of the contact force |
g | Acceleration due to gravity |
Geq | Equivalent shear modulus |
Ii | Moment of inertia of a particle |
k1 | Loading stiffnesses |
k2 | Unloading stiffnesses |
kn | Normal stiffness |
kt | Tangential component of stiffness |
meq | Equivalent particle mass |
mi | Mass of spherical particle |
mr | Mass of the ball used in inclined plane test |
ms | Mass of block used in inclined plane test |
N | N factor. Suffixes: γ = gravitational, c = cohesive, a = adhesive, q = surcharge |
P | Soil cutting force (N) |
q | Surcharge stress (Pa) |
q | Deviator stress in triaxial compression test |
rc | Contact radius |
req | Equivalent particle radius |
ri, | Radius of spherical particle |
Ti | Torque due to the tangential component of the contact force |
Vg | Voidage grid volume |
Vp | Total volume of particles with centroids within voidage grid |
w | Tool width (m) |
xi | Location of spherical particle |
γ | Specific weight of soil (N m−3) |
εa | Axial strain in triaxial compression test |
σ1 | Axial stress in triaxial compression test |
σ3 | Radial stress in triaxial compression test |
Ψ | Inclined plane tilt angle. Subscripts: s = sliding, r = rolling |
ωi | Angular velocity of a particle |
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Contact Model | Advantages | Disadvantages | Types of Soil Modelled | References | Software Used by Researchers |
---|---|---|---|---|---|
Linear spring contact model |
|
| Sandy | Tanaka et al. [27], Asaf et al. [10], Shmulevich et al. [6], Ono et al. [28] | PFC2D, EDEM |
Linear spring contact model with cohesion |
|
| Vertosol | Bravo et al. [18] | DEMeter++ |
Hertz–Mindlin contact model |
|
| Sandy | Ucgul et al. [29] | EDEM |
Parallel bond model (PBM) or Hertz–Mindlin contact model with cohesion |
|
| Coarse sand, loamy, sandy loam, loessal, clay, sandy clay loam, loamy clay | Tamas et al. [30], Chen et al. [7], Bo et al. [31], Hang et al. [32], Cheng et al. [33], Yang et al. [34], Hoseinian et al. [35] | EDEM PFC3D |
Hertz–Mindlin contact model with Johnson–Kendall–Roberts (JKR) |
|
| Clay, silty clay loam | Cheng et al. [33], Du et al. [36], Zhai et al. [37] | EDEM |
Hysteric spring contact model |
|
| Sandy | Ucgul et al. [38], Ucgul et al. [29] | EDEM |
Hysteric spring contact model with linear cohesion contact model |
|
| Sandy loam, clay (Vertosol) | Barr et al. [21], Barr et al. [39], Makange et al. [40], Aikins et al. [41], Awuah et al. [42], Wang et al. [43] | EDEM |
Edinburgh elasto-plastic adhesion model |
|
| Clay, clay loam, sandy loam, loam, sandy | Kim et al. [44], Wu et al. [45], Zhao et al. [46], Sun et al. [47] | EDEM, PFC3D, LiGGGHTS |
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Aikins, K.A.; Ucgul, M.; Barr, J.B.; Awuah, E.; Antille, D.L.; Jensen, T.A.; Desbiolles, J.M.A. Review of Discrete Element Method Simulations of Soil Tillage and Furrow Opening. Agriculture 2023, 13, 541. https://doi.org/10.3390/agriculture13030541
Aikins KA, Ucgul M, Barr JB, Awuah E, Antille DL, Jensen TA, Desbiolles JMA. Review of Discrete Element Method Simulations of Soil Tillage and Furrow Opening. Agriculture. 2023; 13(3):541. https://doi.org/10.3390/agriculture13030541
Chicago/Turabian StyleAikins, Kojo Atta, Mustafa Ucgul, James B. Barr, Emmanuel Awuah, Diogenes L. Antille, Troy A. Jensen, and Jacky M. A. Desbiolles. 2023. "Review of Discrete Element Method Simulations of Soil Tillage and Furrow Opening" Agriculture 13, no. 3: 541. https://doi.org/10.3390/agriculture13030541